Reigning European champions Chelsea will face Sparta Prague in the last 32 of the Europa League.
The Blues, who failed to make the knockout stages of the top-tier European competition, will start their bid to become only the fourth club after Juventus, Ajax and Bayern Munich to win all of the major European trophies.
Tottenham will take on Ligue 1 side Lyon, starting with a home tie on February 14, while Liverpool face Russian champions Zenit St Petersburg and Newcastle take on Ukraine's Metalist Kharkiv.
Chelsea avoided a rematch with Atletico,.who handed them a 4-1 drubbing in the Super Cup back in August, and as a seeded team will start their Europa League campaign in Prague.
Atletico drew Russian side Rubin Kazan as they bid to defend the title they won with a comprehensive 3-0 defeat of Athletic Bilbao in last year's all-Spanish final.
Liverpool travel to Zenit for their opening round of 32 match to face the Russian side who has hit the headlines this week when their largest supporters group, Landscrona, caused widespread outrage.
They posted an open letter on their website that outlined their preferred criteria for future signings at Zenit to exclude sexual minorities and non-Europeans from the playing staff.
Tottenham will play what could be one of the most hotly contested ties of the round when they face Lyon, who are a tough opponent more used to Champions League football.
Andre Villas-Boas' side could line up a last-16 meeting with Inter Milan if they can beat Lyon over two legs, and if the Serie A side can win their tie against Romania's Cluj.
It would be a much-anticipated match an evoke memories of when Gareth Bale scored a hat-trick at the San Siro for Tottenham against Inter in a match that eventually saw the north London side lose 4-3 in October 2010.
Draw for the Europa League round of 32:
BATE Borisov v Fenerbahce
Inter Milan v CFR Cluj
Levante v Olympiakos Piraeus
Zenit St Petersburg v Liverpool
Dynamo Kiev v Girondins Bordeaux
Bayer Leverkusen v Benfica
Newcastle United v Metalist Kharkiv
VfB Stuttgart v Racing Genk
Atletico Madrid v Rubin Kazan
Ajax Amsterdam v Steaua Bucharest
Basel v Dnipro Dnipropetrovsk
Anji Makhachkala v Hanover 96
Sparta Prague v Chelsea
Borussia Moenchengladbach v Lazio
Tottenham Hotspur v Olympique Lyon
Napoli v Viktoria Plzen
Draw for the Europa League round of 16:
Napoli/Plzen vs BATE/Fenerbahce
Bayer Leverkusen/Benfica vs Dynamo Kiev/Bordeaux
Anzhi Mackhachkala/Hannover 96 vs Newcastle/FC Metalist Kharkiv
VfB Stuttgart/Genk vs Borussia M'gladbach/Lazio
Tottenham/Lyon vs Inter Milan/CFR Cluj-Napoca
Levante/Olympiacos vs Atletico Madrid/Rubin Kazan
Basle/Dnipro vs Zenit St Petersburg/Liverpool
Ajax/Steaua Bucuresti vs Sparta Prague/Chelsea